I'm supposed to plot (x1 vs x2) for a system. (Dynamics and Controls)

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PVR 2014-11-12

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https://ww2.mathworks.cn/matlabcentral/answers/162459-i-m-supposed-to-plot-x1-vs-x2-for-a-system-dynamics-and-controls

评论： Star Strider 2014-11-13

I have a system in state space model x'=Ax where A = [0 1; -14 -4]. The system quation is x(t) = e^At*x(0) where given x(0) is [-0.2; 0.2] Now I'm supposed to solve for x(t) which gives a matrix [x1(t);x2(t)] and plot the graph of the elements x1(t) vs x2(t) which is also known as Phase portrait. I believe its a simple code but I'm going wrong somewhere. Can you help me where and what's wrong? Any help is appreciated. Thank you!

    A=[0 1;-14 -4];
t=linspace(0,10,300);
x=zeros(2,300);
matA = zeros(2,2,300);
x0 = [-0.2;0.2];
for k=1:300, matA(:,k) = expm(A*t(k)); x(:,k) = matA(:,k)*x0;end;
plot(x(:,1),x(:,2))

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采纳的回答

Star Strider 2014-11-13

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https://ww2.mathworks.cn/matlabcentral/answers/162459-i-m-supposed-to-plot-x1-vs-x2-for-a-system-dynamics-and-controls#answer_158733

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You’re almost there. You did everything correctly, but you need a ‘C’ output matrix (part of the ‘ABCD’ matrices in a state space system). I added one I considered appropriate to your problem, and since this creates ‘x’ as a (2x300) array, I changed the plot references to reflect that:

A=[0 1;-14 -4];
t=linspace(0,10,300);
x=zeros(2,300);
matA = zeros(2,2,300);
x0 = [-0.2;0.2];
C = [1 0; 0 1];
for k=1:300, 
    matA(:,:,k) = expm(A*t(k)); 
    x(:,k) = C*matA(:,:,k)*x0;
end
figure(1)
plot(x(1,:),x(2,:))
grid